# Document 15937261

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```The following kinetic equations can therefore be used
describe growth under oxygen limited conditions.
 m Co
dX

X
dt K o  Co
dCo
1  m Co

X
dt
Yo K o  Co
Where Co is the concentration of oxygen, &micro;m is the maximum
specific growth rate, Yo is the biomass yield from oxygen and
Ko is the Monod constant for oxygen uptake.
1
Thus the oxygen uptake rate (OUR) can be described the
equation:
1  m Co
OUR 
X
Yo K o  Co
The dissolved oxygen concentration in a reactor is thus
determined by the balance between the oxygen transfer
rate (OTR) and oxygen uptake rate (OUR).
dCo
 OTR  OUR
dt
dCo
1  m Co
*
 k L a Co  Co  
X
dt
Yo K o  Co
2
Steady state analysis
The movement of
oxygen from a bubble
through the bulk liquid
to a cell, can be
thought of as a
continuous process.
Oxygen enters the
bulk liquid and is
removed by the cells.
3
The dissolved oxygen concentration in the bulk
liquid will quickly reach a steady state and
therefore
dCo
0
dt
and the oxygen transfer rate will equal the oxygen
uptake rate
OTR = OUR
1  m Co
k L a C  Co 
X
Yo K o  Co

*
o

4
Critical Oxygen Concentration
• Co,cr is the
concentration of
dissolved oxygen
below which a
culture is oxygen
limited.
• Then &micro; = &micro;m , the
cells are not
oxygen limited.
5
Integrating the oxygen uptake
and oxygen transfer equations
The steady state relationship between oxygen
uptake and oxygen transfer:
OTR = OUR
1  m Co
k L a C  Co 
X
Yo K o  Co

*
o

6
level of mixing
7
Medium viscosity
8
Temperature
9
Interfacial area and
oxygen transfer

10
```